Programmable Re-entrant Topological Polaritons in Graphene Grating/α-MoO₃ Heterostructure

Achieving active, multistate control over the topology of in-plane polaritons is crucial for developing advanced nanophotonic devices, yet existing platforms are fundamentally limited by intrinsic structures of natural materials or restricted tuning mechanisms. Here, we overcome these limitations by introducing a graphene grating/α-MoO₃ heterostructure that merges static, synthetic geometric design with dynamic tuning via doping. By engineering the interaction between the intrinsic anisotropy of α-MoO₃ and the tunable synthetic anisotropy of the graphene metasurface, we realize a doping-driven re-entrant topological transition (Hyperbolic-Elliptic-Hyperbolic). Moreover, we show that the system can be designed to exhibit a predetermined number of topological transitions by geometrically setting the fill factor of the grating. Finally, by rotationally misaligning the two anisotropic axes, we experimentally validate tilted, asymmetric polaritons and vortex-like patterns via s-SNOM. This work establishes a framework for programming polaritonic topology, directionality, and symmetry, opening a route toward advanced reconfigurable nanophotonic devices.